Canon 40d won't turn on, LCD is blank.

There are several different things that can cause the camera to not start up. Refer to your user manual to check each of these items. If you don't have your user manual, you can download it here.

1) The battery is not properly installed in the camera. (p.26)
2) Make sure the battery compartment cover is closed. (p.26)
3) Make sure the CF card slot cover is closed. (p.28)

In addition, the battery may not have been properly recharged. Double check that the charger is plugged into a working outlet, and double check that it shows that the battery is fully charged.

If none of these fix the problem then you have a defective camera - one of the switches for the battery compartment or the CF card slot cover may be not properly indicating that the door is closed. If that's the case, you need to either return it to the place of purchase as defective, or send it in to Canon for warranty repair.